DUNE PDELab (2.7)

Setting up blocked data structures

When solving vector-valued PDEs the result at each grid point must be a vector. When doing this the ordering of the global indices can be chosen, e.g. lexicographic or entity blocked. For many solvers, e.g. AMG, the ordering makes a difference in the efficiency of the solver. Further options, such as choosing to aggregate over the blocks and specifying the norm to be used can produce faster results.

First, we have to define one or more scalar grid function spaces to combine

// Set up scalar grid function space
SCALAR_GFS U1(grid.leafGridView(),fem); U1.name("U1");
SCALAR_GFS U2(grid.leafGridView(),fem); U2.name("U2");
A grid function space.
Definition: gridfunctionspace.hh:186

There are two ways to define a vector-valued grid function space. If all scalar grid function spaces are the same a power grid function space can be used. In contrast a composite grid function space allows for different scalar grid function spaces. Both can be used with different blocking.

Let's first define a power grid function space with lexiographic ordering

// Use lexiographical blocked ordering
typedef Dune::PDELab::LexicographicOrderingTag LexiographicOrderingTag;
// Set up power grid function space
using VBE = Dune::PDELab::ISTL::VectorBackend<Dune::PDELab::ISTL::Blocking::fixed>; // blocking vector backend
dim, // block size
VBE, // blocked vector backend
LexiographicOrderingTag> GFS;
GFS gfs(U1,U2);
base class for tuples of grid function spaces product of identical grid function spaces base class th...
Definition: powergridfunctionspace.hh:49
Indicate lexicographic ordering of the unknowns of non-leaf grid function spaces.
Definition: tags.hh:63

And then a composite grid function space with entity blocked ordering

// Use entity blocked ordering
typedef Dune::PDELab::EntityBlockedOrderingTag EntityOrderingTag;
// Setting up a composite grid function space with the same scalar grid function space in both components
using VBE = Dune::PDELab::ISTL::VectorBackend<Dune::PDELab::ISTL::Blocking::fixed>; // blocking vector backend
typedef Dune::PDELab::CompositeGridFunctionSpace<VBE, // blocked vector backend
EntityOrderingTag,
SCALAR_GFS, SCALAR_GFS> GFS;
GFS gfs(U1,U2);
base class for tuples of grid function spaces base class that holds implementation of the methods thi...
Definition: compositegridfunctionspace.hh:53
Indicate blocking of the unknowns by grid entity.
Definition: tags.hh:53

Full example code: recipe-blocking.cc

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